1. Field of the Invention
The present invention relates to data processing method and program suitable for use in Response Surface Methodology (RSM) which effectively utilizes less experimental data to enhance design efficiency. Particularly, the present invention relates to data processing method and program capable of estimating obtained curve or surface model and the like.
2. Description of Related Art
Recent heightening of user requirements, intensification of competition in the marketplace, and the introduction of cheap foreign products have all resulted in increased market demands in the areas of product quality, delivery, and costing. Furthermore, there are demands for both increased efficient in product and productivity planning, and for reduced development costs. In response to these demands, recent years have seen more interest in response surface methodology, a technology for efficient implementation of design tasks that require high amounts of experimentation.
Japanese Unexamined Patent Application Publication No. 2002-18311, which is referred to herein as the related art 1, for example, contains disclosure concerning a method that efficiently identificates a response surface model by biharmonic spline interpolation based on the Green function with the use of data collected according to the experimental design. The response surface model is used in Response Surface Methodology (RSM) for pharmaceutical design, materials design, design or adjustment of system operating conditions and product manufacturing conditions and the like.
The use of the response surface model generated by the biharmonic spline interpolation based on the Green function described in the related art 1 enables easy finding of optimum design conditions. It is thereby possible to find optimum design conditions quickly from a small amount of experimental data even for a complex and unknown design target.
Yutaka Tanaka et al. “Handbook of Statistical Analysis”, 1995, pp. 22-24 describes that, where a correlation (responce) between design conditions and product characteristics is expressed by a linear polynominal (linear regression model), it is possible to estimate variations in a response surface model based on a statistical approximate error and thus possible to estimate the reliability of an optimum solution.
A conventional response surface model generation and estimation method where a response surface model is a linear regression model is described herein. FIG. 11 is a block diagram showing a conventioal response surface model estimation apparatus 100. The response surface model estimation apparatus 100 includes an experimental data DB 101 for storing experimental data, a response surface model generation section 102, an optimum solution search section 103, a response surface model estimation section 104, and an optimum solution estimation index calculation section 105. The response surface model generation section 102 generates a response surface model, which is a linear regression model, from the experimental data stored in the experimental data DB 101. The optimum solution search section 103 searches for an optimum solution of the generated surface model. The response surface model estimation section 104 calculates F value, which is described below, from the response surface model. The optimum solution estimation index calculation section 105 calculates an estimation index from the optimum solucion obtained by the optimum solution search section 103 and the F value calculated by the response surface model estimation section 104.
The conventional response surface model estimation apparatus 100 obtains an estimation index of the reliability of an optimum solution based on the approximation accuracy of a response surface model identificated from experimental data, which is goodness of fit of a regression model to data (F value in the following equation 1):
                    F        =                              V            R                                V            e                                              (        1        )            where, when     y is the mean of n-number of data items of response variable y;    ŷ is the estimate by a regression model; and    p is the degree of freedom,parameter variation:
            V      R        =                            ∑                      i            =            1                    n                ⁢                              (                                                            y                  ^                                i                            -                              y                _                                      )                    2                    p        ,and model accuracy:
      V    e    =                              ∑                      i            =            1                    n                ⁢                              (                                          y                i                            -                                                y                  ^                                i                                      )                    2                            (                  n          -          p          -          1                )              .  
However, the application of the estimation based on a statistical approximate error in the case where a response surface model is a linear regression model is limited to partucular targets. The estimation method cannot be applied to a target with a complex correlation (responce) between design conditions and product characteristics, like a non-linear response surface as described in the related art 1. This means that there is no solution estimation means for a technique described in the related art 1, though actual product design needs to make allowances for variations in optimum conditions (optimum solution).